LMFDB - L-function search results

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Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank

Degree	Bad $p$	Root analytic conductor	Motivic weight	Spectral label

Root angle	Primitive	Origin	Exclude origin	Self-dual

Arithmetic

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Results (1-50 of 227 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-916-916.107-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.107	$0$	✓	✓	$-0.239$	$0$	$0.526397$	Character $\chi_{916}(107, \cdot)$
1-916-916.115-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.115	$0$	✓	✓	$-0.297$	$0$	$0.241839$	Character $\chi_{916}(115, \cdot)$
1-916-916.119-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.119	$0$	✓	✓	$-0.327$	$0$	$0.954330$	Character $\chi_{916}(119, \cdot)$
1-916-916.123-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.123	$0$	✓	✓	$0.0303$	$0$	$1.32602$	Character $\chi_{916}(123, \cdot)$
1-916-916.127-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.127	$0$	✓	✓	$0.214$	$0$	$1.23101$	Character $\chi_{916}(127, \cdot)$
1-916-916.131-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.131	$0$	✓	✓	$-0.0189$	$0$	$1.23954$	Character $\chi_{916}(131, \cdot)$
1-916-916.139-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.139	$0$	✓	✓	$-0.129$	$0$	$0.879692$	Character $\chi_{916}(139, \cdot)$
1-916-916.143-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.143	$0$	✓	✓	$0.0205$	$0$	$1.21630$	Character $\chi_{916}(143, \cdot)$
1-916-916.155-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.155	$0$	✓	✓	$-0.111$	$0$	$0.478501$	Character $\chi_{916}(155, \cdot)$
1-916-916.163-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.163	$0$	✓	✓	$0.396$	$0$	$1.67257$	Character $\chi_{916}(163, \cdot)$
1-916-916.175-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.175	$0$	✓	✓	$-0.288$	$0$	$0.571590$	Character $\chi_{916}(175, \cdot)$
1-916-916.179-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.179	$0$	✓	✓	$-0.208$	$0$	$0.457552$	Character $\chi_{916}(179, \cdot)$
1-916-916.191-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.191	$0$	✓	✓	$-0.231$	$0$	$0.607370$	Character $\chi_{916}(191, \cdot)$
1-916-916.195-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.195	$0$	✓	✓	$0.0688$	$0$	$1.16474$	Character $\chi_{916}(195, \cdot)$
1-916-916.199-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.199	$0$	✓	✓	$0.156$	$0$	$1.11230$	Character $\chi_{916}(199, \cdot)$
1-916-916.207-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.207	$0$	✓	✓	$0.121$	$0$	$0.882728$	Character $\chi_{916}(207, \cdot)$
1-916-916.211-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.211	$0$	✓	✓	$0.0296$	$0$	$1.12004$	Character $\chi_{916}(211, \cdot)$
1-916-916.219-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.219	$0$	✓	✓	$0.141$	$0$	$1.48583$	Character $\chi_{916}(219, \cdot)$
1-916-916.223-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.223	$0$	✓	✓	$0.429$	$0$	$1.19843$	Character $\chi_{916}(223, \cdot)$
1-916-916.227-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.227	$0$	✓	✓	$-0.117$	$0$	$0.924906$	Character $\chi_{916}(227, \cdot)$
1-916-916.23-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.23	$0$	✓	✓	$-0.291$	$0$	$0.879362$	Character $\chi_{916}(23, \cdot)$
1-916-916.231-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.231	$0$	✓	✓	$0.297$	$0$	$1.42071$	Character $\chi_{916}(231, \cdot)$
1-916-916.235-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.235	$0$	✓	✓	$0.231$	$0$	$0.993541$	Character $\chi_{916}(235, \cdot)$
1-916-916.239-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.239	$0$	✓	✓	$0.291$	$0$	$1.97026$	Character $\chi_{916}(239, \cdot)$
1-916-916.247-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.247	$0$	✓	✓	$0.0507$	$0$	$1.02479$	Character $\chi_{916}(247, \cdot)$
1-916-916.251-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.251	$0$	✓	✓	$-0.229$	$0$	$0.327148$	Character $\chi_{916}(251, \cdot)$
1-916-916.259-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.259	$0$	✓	✓	$-0.359$	$0$	$0.726361$	Character $\chi_{916}(259, \cdot)$
1-916-916.263-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.263	$0$	✓	✓	$0.0101$	$0$	$0.742228$	Character $\chi_{916}(263, \cdot)$
1-916-916.267-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.267	$0$	✓	✓	$-0.429$	$0$	$0.376442$	Character $\chi_{916}(267, \cdot)$
1-916-916.279-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.279	$0$	✓	✓	$0.482$	$0$	$1.44058$	Character $\chi_{916}(279, \cdot)$
1-916-916.283-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.283	$0$	✓	✓	$-0.0303$	$0$	$1.09352$	Character $\chi_{916}(283, \cdot)$
1-916-916.295-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.295	$0$	✓	✓	$0.305$	$0$	$1.62608$	Character $\chi_{916}(295, \cdot)$
1-916-916.303-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.303	$0$	✓	✓	$0.359$	$0$	$0.841483$	Character $\chi_{916}(303, \cdot)$
1-916-916.31-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.31	$0$	✓	✓	$0.0515$	$0$	$1.24804$	Character $\chi_{916}(31, \cdot)$
1-916-916.315-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.315	$0$	✓	✓	$-0.0960$	$0$	$1.15323$	Character $\chi_{916}(315, \cdot)$
1-916-916.319-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.319	$0$	✓	✓	$0.317$	$0$	$1.20362$	Character $\chi_{916}(319, \cdot)$
1-916-916.327-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.327	$0$	✓	✓	$-0.300$	$0$	$0.752662$	Character $\chi_{916}(327, \cdot)$
1-916-916.331-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.331	$0$	✓	✓	$0.327$	$0$	$1.70706$	Character $\chi_{916}(331, \cdot)$
1-916-916.335-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.335	$0$	✓	✓	$0.288$	$0$	$1.69911$	Character $\chi_{916}(335, \cdot)$
1-916-916.339-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.339	$0$	✓	✓	$-0.214$	$0$	$0.884551$	Character $\chi_{916}(339, \cdot)$
1-916-916.343-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.343	$0$	✓	✓	$0.117$	$0$	$0.982858$	Character $\chi_{916}(343, \cdot)$
1-916-916.35-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.35	$0$	✓	✓	$0.181$	$0$	$1.24394$	Character $\chi_{916}(35, \cdot)$
1-916-916.351-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.351	$0$	✓	✓	$0.239$	$0$	$1.04382$	Character $\chi_{916}(351, \cdot)$
1-916-916.371-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.371	$0$	✓	✓	$-0.482$	$0$	$0.360795$	Character $\chi_{916}(371, \cdot)$
1-916-916.379-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.379	$0$	✓	✓	$0.0133$	$0$	$0.838427$	Character $\chi_{916}(379, \cdot)$
1-916-916.39-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.39	$0$	✓	✓	$-0.224$	$0$	$0.763560$	Character $\chi_{916}(39, \cdot)$
1-916-916.391-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.391	$0$	✓	✓	$0.278$	$0$	$0.152636$	Character $\chi_{916}(391, \cdot)$
1-916-916.395-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.395	$0$	✓	✓	$-0.438$	$0$	$0.363452$	Character $\chi_{916}(395, \cdot)$
1-916-916.399-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.399	$0$	✓	✓	$-0.396$	$0$	$0.623061$	Character $\chi_{916}(399, \cdot)$
1-916-916.411-r0-0-0	$4.25$	$4.25$	$1$	$2^{2} \cdot 229$	916.411	$0$	✓	✓	$-0.402$	$0$	$0.0563366$	Character $\chi_{916}(411, \cdot)$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.